Modern model predictive control schemes are based on discrete-time linear stochastic state-space models. The state is reconstructed from measurements using a Kalman filter and the outputs are predicted by a Kalman predictor. The performance of the controller will depend on the accuracy of the state estimates. However, information about process noise and measurement noise statistics is required for tuning of the Kalman filter. Tuning the filter manually represents a considerable burden for the user. In addition, the process may be affected by unknown disturbances and identifying them requires skill and experience. Therefore there is a clear need for a tool that can perform filter tuning and disturbance identification or provide assistance to the user. The control performance will improve as a result of the increased accuracy of the state estimates.

The filter tuning problem is essentially a covariance estimation problem in which the Kalman filter gain is computed based on the estimated covariances. The autocovariance least-squares (ALS) method is used to compute a least-squares estimate of the noise covariance matrices based on the estimated autocovariance of the output innovations (Odelson et al., 2006a). The estimation problem can be stated in the form of a convex semidefinite program, which can be solved by interior-point methods which guarantee positive semidefiniteness of the covariance matrices. An advantage of the approach is that routine operating data from the process can be used.

The ALS method can also account for plant-model mismatch and unknown disturbances (Odelson et al., 2006b). A standard procedure for achieving offset-free model predictive control is to augment the model with integrating white-noise disturbances. The covariance of the noise in the disturbance model can be estimated along with the covariance of the process noise and measurement noise.

The improvement in control performance after applying the tuning procedure is demonstrated on systems controlled by model predictive control. Results from both numerical examples and a laboratory-scale quadruple tank process are presented.

References:

Odelson, B. J., Rajamani, M. R., and Rawlings, J. B., (2006a). A new autocovariance least-squares method for estimating noise covariances, Automatica, 42(2), 303–308.

Odelson, B. J., Lutz, A., and Rawlings, J. B., (2006b). The autocovariance least-squares method for estimating covariances: Application to model-based control of chemical reactors, IEEE Transactions on Control Systems Technology, 14(3), 532-540.